Drawing from the broad spectrum of phenomena, described in more than 100,000 articles on high-Tc superconductivity, in this book, the authors analyze those basic properties for which understanding can be achieved within the framework of traditional methods of theoretical physics. This is the case of the overdoped cuprates for which the "Bardeen program" has been realized: We know their electronic spectrum, we can calculate their basic thermodynamic and electrodynamic properties, and predict new phenomena. The book gives a pedagogical derivation of formulas describing the electron band structure, penetration depth, specific heat, fluctuation conductivity, etc. Prediction of plasmons and their application for a new type of THz generators is considered as well. The book advocates that the strongest exchange interaction in condensed matter physics -- the intraatomic s-d exchange -- is the long sought pairing mechanism in overdoped cuprate superconductors The main focus of the book is to present the effects of nanostructuring on superconducting critical parameters. Optimizing systematically flux and condensate confinement in various nanostructured superconductors, ranging from single nano-cells to their huge arrays, critical fields and currents can be increased up to their theoretical limits, thus drastically improving the potential for practical applications of nanostructured superconductors. Read more... 1. Introduction. 1.1. Quantization and confinement in nano-materials. 1.2. Nanostructuring. 1.3. Confining the superconducting condensate. 1.4. Nucleation of superconductivity in presence of spatially modulated magnetic fields. 1.5. Vortex matter in superconductors. 1.6. Flux pinning -- 2. Individual nanostructures. 2.1. Line. 2.2. Loop. 2.3. Disc. 2.4. The cross-over from loop to dot. 2.5. Symmetry-induced antivortices in mesoscopic superconductors. 2.6. The magnetization of singly connected nanostructures. 2.7. Dynamic effects in mesoscopic structures. 2.8. Hybrid individual cells -- 3. Clusters of nanocells. 3.1. One-dimensional clusters of loops. 3.2. Two-dimensional clusters of antidots. 3.3. Magnetically coupled loops -- 4. Laterally nanostructured superconductors. 4.1. The Tsymbol phase boundary of superconducting films with an antidot lattice. 4.2. Pinning in laterally nanostructured superconductors. 4.3. Ratchet effects in antidot lattices -- 5. Superconductor-ferromagnet hybrid systems. 5.1. Field polarity dependent vortex pinning in laterally nanostructured S/F systems. 5.2. Field induced superconductivity. 5.3. Dipole-induced vortex ratchet effects. 5.4. Superconductivity in stray fields of magnetic domains